Interface Dosimetry for Electronic Brachytherapy Intracavitary Breast Balloon Applicators

Transcription

1 Interface Dosimetry for Electronic Brachytherapy Intracavitary Breast Balloon Applicators J.J. Segala 1, G.A. Cardarelli 2, J.R. Hiatt 2, B.H. Curran 2, E.S. Sternick 2 1 Department of Physics, University of Rhode Island, 2 Lippitt Road, Kingston, RI Department of Radiation Oncology, Rhode Island Hospital/Brown University Medical School,, 593 Eddy St., Providence RI Key Words: accelerated partial breast irradiation, electronic brachytherapy, monte carlo simulation, ABSTRACT PURPOSE: To evaluate the dose distribution in the region between the surface of the Xoft, Inc. Axxent electronic brachytherapy (EBT) barium-impregnated balloon applicator for accelerated partial breast irradiation (APBI) and the prescription point at 1cm depth in tissue. METHODS: Depth dose curves were generated for a range of balloon wall thicknesses. Numerical data were verified with experimental readings using a parallel plate extrapolation ionization chamber, which allowed for maximum surface dose measurement accuracy. For several source dwell positions, a dose distribution was calculated using a general purpose multi particle transport code (FLUKA). Treatment planning dose distributions were generated using TG-43 methods, with anisotropy and radial dose functions provided by the company. RESULTS: Dose distributions for several Axxent balloon shapes and sizes were computed using numerical and experimental methods and then compared with dose distributions from a commercial treatment planning system. The results for the 5x7 cm ellipsoidal balloon applicator are given for five different source dwell positions. At the 1.0 cm prescription line, the dose distribution differed only slightly. However, at the balloon s surface, the actual dose was found to be as much as 1.5 times greater than the dose determined by the treatment planning system (TPS). CONCLUSIONS: The Xoft Axxent system uses a 6.0% correction factor to planned treatment times to account for balloon wall attenuation. By applying this universal factor, however, the dose distribution throughout the entire planned volume is uniformly affected. The AAPM TG-43 source data currently incorporated by commercially available treatment planning systems do not account for the variable dose distributions attributable to balloon wall attenuation. Our results show that variable attenuation factors should be applied in order to determine near-surface dose distributions when using barium impregnated balloons for intracavitary breast brachytherapy. Dose distributions at distances greater than 1 cm from the surface of the balloon appear to be accurately represented without further modification. 1

2 Introduction Xoft, Inc., (Sunnyvale,CA.), recently introduced a technique for administering Accelerated Partial Breast Irradiation (APBI) [1] that employs a low energy, 50-kV, electronic radiation source administered through a balloon applicator implanted in the tumor cavity and inflated with saline solution. To deliver a prescribed radiation dose, the Axxent controller moves the radiation source through the balloon catheter, stopping at a series of dwell positions for pre-determined times. These dwell positions and times are computed using a commercially available brachytherapy treatment planning system and transferred to the Axxent controller. The treatment planning methodology used in EBT is similar to that of high dose radiotherapy (HDR) with Iridium-192. For EBT, the manufacturer provides specialized TG-43 parameters [2] [3] including active source length, air kerma strength, dose rate constant, radial dose function, and anisotropy function. A line source approximation is assumed. In order to facilitate the treatment of different tumor bed shapes and sizes, balloon applicators are available in sizes ranging from 4 to 6 cm spherical and 5x6 cm and 5x7 cm ellipsoidal. The balloon portion of the applicator is made from a proprietary siliconebased material impregnated with barium sulfate. The barium is introduced into the balloon material to allow the balloon to fluoresce during imaging and treatment simulation. However, during a treatment, the barium absorbs some of the ionizing radiation, to a greater degree than an equivalent thickness of water, thereby attenuating the planned patient dose. To demonstrate this phenomenon, Fig 1 is a comparison of the scattering amplitudes for photons and the stopping power for electrons for the barium impregnated balloon material and water [5] [6]. The barium impregnated balloon material has a larger scattering amplitude and stopping power than does an equivalent amount of water, suggesting that more energy will be absorbed by the balloon material than would be absorbed by the same thickness of water in the energy range of the source spectrum, thus restricting the passage of ionizing radiation through the balloon wall to the patient. 2

3 Fig 1: Scattering amplitude and Stopping Power versus energy for the barium impregnated balloon material compared to water. Since the treatment planning system utilizes a homogenous-medium dose calculation and does not consider attenuating material in the radiation path, resulting computed doses will be inaccurate unless appropriately modified. The manufacturer accounts for the balloon wall attenuation by applying a universal correction factor and increasing all the computed dwell times by 6.0%. This factor was derived by measuring the dose at 1.0 cm from the balloon surface, in a water phantom, in the presence and absence of the silicon material and comparing the two results. A single correction factor, however, does not account for all variables that influence the dose distribution. For example, the thickness of the balloon material at different polar angles will play a large role in determining the attenuation due to differences in scattering amplitude and stopping power. This study was conducted to gain additional knowledge about the true dose distribution of low energy radiation that passes through several centimeters of saline and various thicknesses of barium-impregnated balloon material before entering the patient s tissues. The results for multiple dwell position combinations were compared to dose distributions computed by a commercial treatment planning system and a realistic attenuation field determined. Methods and materials Numerical and experimental analyses were conducted to determine the dose distribution for the various Axxent balloon shapes and dwell positions. The extent of the experimental investigation was limited to a subset of all the data accumulated as a verification of the numerical accuracy. It was assumed that when the balloon is maximally inflated, its thickness at the apex, normal to the central catheter, is approximately 0.3 mm and thickens to approximately 0.55 mm at the distal and proximal ends. Experimental data for thicknesses of 0.4 mm 3

4 and 0.5 mm were obtained to verify the numerical results for the full span of thicknesses needed for the analysis. A. Experimental Measurements A Far West Technologies plane parallel plate extrapolation ionization chamber, model EIC-1, was used to determine dose in the build-up region near the surface [7]. Measurements of the radiation were taken with 1.3, 2.3, 3.3, and 4.3 mm electrode separations and the surface dose estimated by extrapolating these readings to a zero mm electrode separation. The bias voltage was adjusted to maintain a 50V/mm potential between the electrodes. As a consequence of the Compton Effect, electrons ejected from the lower electrode of the ionization chamber add positive current to the electrometer reading. As the electrodes are brought closer this effect becomes more pronounced. To correct for this phenomenon, two dose readings with opposite bias polarity were obtained and the results averaged. The experimental setup simulated a Xoft Axxent x-ray source positioned 2.5 cm from the balloon s outer wall with wall thicknesses of 0.4 mm and 0.5 mm. The extrapolation chamber was set at 0, 2.0, 4.0, 6.0, and 10.0 mm distant from the wall to obtain depth dose readings. The balloon material was stretched to the desired thickness and fastened to a 30 cm x 30 cm x 5 cm thick Solid Water phantom. The extrapolation chamber was placed in another 30 cm x 30 cm x 5 cm thick Solid Water phantom. Slice thicknesses of 0, 2.0, 4.0, 6.0, and 10.0 mm Solid Water were positioned between the two 5.0 cm slabs, as pictured in Fig 2. and measurements obtained for each slab thickness. Xoft Source Solid Water 30 x 30 x 5 cm Balloon Material.5 mm Thick 2.5 cm Solid Water 30 x 30 x 5 cm Far West Tech Extrapolation Chamber Solid Water 0,2,4,6,10 mm Thick Fig 2 : Experimental setup showing the placement of the Xoft Axxent X-Ray Source, balloon material, and the extrapolation chamber. 4

5 To understand the effects of the interposed balloon material on the dose distribution, a second set of readings was taken with a water equivalent material of the same thickness, positioned in place of the balloon material with no dimensional changes to the setup shown in Fig 2. Finally, a check with a balloon thickness of 0.4 mm was performed with readings taken at depths of 2.0 mm and 10.0 mm. B. Numerical Analysis To perform the numerical calculations, a general purpose multi particle transport code (FLUKA) was used. FLUKA, which is supported by the European Organization for Nuclear Research (CERN), is a numerical tool for the calculation of particle transport and interactions with matter. It is designed for applications that include shielding, calorimetry, dosimetry, detector design, and radiotherapy. Fig 3 shows a typical arrangement of the Xoft Axxent source and balloon. However, source position and the shape of the balloon are variable. Water Phantom Dose Point Balloon Catheter r Ө Xoft Axxent X-Ray Source Dwell Position Axxent Balloon Applicator Fig 3 : Numerical model used for the analysis of the balloon material. The x-ray radiation source is shown in the central dwell position but may be positioned at any of the possible dwell positions. The dose point is referenced by specifying the radial position, r, and polar angle Ө from the dwell position. To proceed with the numerical analysis, the energy spectrum of the Xoft source was determined at various polar angles, Ө. To accomplish this, an accurate model of the 5

6 source was constructed and the energy spectrum at angles ranging from 0 to 180 in 5 increments was computed using FLUKA. Examples of the spectra for Ө = 30, 90, and 150 are shown in Fig 4. The energy spectra for the 36 angles (not all shown) agreed well with the manufacturer s reported spectra [4]. Fig 4 : Sample of the energy spectrum calculated using FLUKA for the numerical analysis. The spectra are normalized at Ө = 90 and energy = 23 kev. As a result of using a low energy source, the thickness of the balloon material traversed by the photons greatly affects the amount of radiation absorbed by the balloon. Therefore, the thickness of the balloon material as a function of the polar angle, Ө was determined. This information was obtained by observing that the thickness of the balloon is approximately proportional to the hoop stress of the inflated balloon at that angle and is also closely proportional to the cosine of the slope of the surface. Therefore, the thickness of the balloon as a function of polar angle can be approximated using this method (Fig 5). In addition, the source dwell position plays a significant role in determining the amount of balloon material through which photons must travel, due to the angle of incidence between the radiation direction and the balloon surface. This is particularly true when the dwell position is close to the distal or proximal ends of the balloon. 6

7 Fig 5 : Plot of the functions to determine the thickness of the applicator balloon material as a function of polar angle Ө normal to the surface. Several FLUKA simulations were performed at various balloon wall thicknesses, and the dose as a function of distance from the balloon wall recorded. In order to compare these results to treatment planning system generated doses, a two-dimensional dose distribution (assuming azimuthal symmetry) is required and was created by tracing rays from the source position to each pixel in a two dimensional graph. Along its path, the ray passes though a length of saline, a thickness of balloon material, and a length of tissueequivalent material (water). The thickness of balloon through which the ray moves is computed using the thickness curves from Fig 5 as well as the angle of incidence of the ray on the balloon wall. An example of the geometry considered, in order to compute the thickness of the balloon material traversed by a ray, is demonstrated in Fig 6. 7

8 Dose Evaluation Point Tissue Equivalent Material Thickness Normal to Surface Saline Balloon Wall Ө Actual Balloon Wall Thickness Traversed X-Ray Beam X-Ray Source Fig 6: Example of the geometry used to compute the actual thickness of balloon material a ray traverses on the path to a dose point. Once the traversed thickness is found, the actual depth dose is determined by interpolating the calculated depth dose curve. The interpolated curve is scaled by the relative energy spectrum which is a function of the polar angle, Ө, from the source dwell position. The dose distribution created by a treatment planning system is also required to determine differences between actual and planned dose. The treatment planning system dose distribution was created with the TG-43 formulation for line source approximation [3]. This requires using the line source geometry function G L (r,ө) along with the anisotropy function F L (r, Ө), and the radial dose function g L (r) provided by Xoft [4]. Results To confirm the accuracy of the numerical model, the setup of the experimental analysis was duplicated numerically and the two results compared. Fig 7 shows the percent depth dose curves as measured experimentally and computed numerically for a balloon wall thickness of 0.5 mm, with and without the balloon applicator material. The depth dose curves were normalized to 1.0 cm for the case without the balloon material. The numerical results are within the error bars of the experimental results. This was also true for the case when the balloon material was stretched to a thickness of 0.4 mm. The depth dose curves for balloon thicknesses 0.3, 0.4, 0.5, and 0.6 mm were computed numerically with the results shown in Fig 8. All depth dose curves are normalized to the 0.3 mm thick curve at 1 cm from the balloon surface. 8

9 Fig 7: Comparison of the experimental results and the numerical results for balloon wall thickness of 0.5 mm plotted as a function of distance from the balloon wall. Fig 8: Depth dose curves for balloon thicknesses 0.3, 0.4, 0.5, 0.6 mm. The curves are normalized at the 0.3 mm thickness at a distance of 1 cm. 9

10 The results for the attenuation of the ionizing radiation as a function of balloon thickness are presented in Fig 9. These curves represent the percent attenuation of the photons as they pass through a layer of balloon material relative to their passage through a water layer of the same thickness. From the graphs, it can be seen that a nominal attenuation of 6.0% is found at the normalization point of 1.0 cm as predicted by Xoft. However, the attenuation is directly proportional to the balloon wall thickness; for a 0.6 mm thick balloon, the attenuation is 18%. As will be demonstrated in a following section, the dose at the surface of the balloon is much larger than is predicated by the treatment planning system. Fig 9 also shows the accuracy of the numerical analysis for both the 0.4 mm and 0.5 mm thicknesses as compared to the experimental results. Fig 9: Attenuation curves for various balloon thicknesses. These curves represent the percent difference of the dose depth curve from the barium impregnated balloon and a equivalent thickness of water. With the results of the analysis of various balloon wall thicknesses, it is possible to build a two-dimensional dose distribution (assuming azimuthal symmetry) for various x- ray source dwell positions. As stated earlier, rays are traced from the source dwell position to each pixel in a two-dimensional graph as seen in the example of Fig 6. Once the traversed thickness is determined, the actual depth dose is obtained by interpolating the depth dose curves from Fig 8. The dose at the point of interest is then computed from the interpolated depth dose curve. 10

11 Fig 10: Dose distribution for a 5x7 ellipsoidal applicator (pictured in gray) for x-ray source dwell positions (black dot) at -2, -1, 0, 1, and 2 cm relative to the center of the applicator. The red dashed line is drawn at 1 cm away from the balloon wall and the red X indicates the normalization location. 11

12 The 5x7 cm ellipsoidal balloon applicator was investigated first to determine the dose distribution at dwell positions -2.0, -1.0, 0, 1.0 and 2.0 cms relative to the center of the applicator. Additionally, the dose distribution generated by the treatment planning system is displayed and the percent difference plotted (Fig. 10). The dose distributions were normalized to 100% at a point which was 1 cm away from the balloon wall and where the treatment planning system computed dose was at its maximum. This point is indicted on the graphs with a red X. For comparison, a 1 cm prescription line is drawn as a red dotted line around the applicator. The balloon applicator is shown as a solid gray object. Discussion The actual dose distribution was computed for an Axxent balloon applicator for various x-ray source dwell positions. Dose distributions were also generated using the TG-43 methodology at the same source dwell positions and the two distributions compared. The dose at 1.0 cm from the balloon surface (red dashed line in Fig 10) has an approximately equivalent dose when the dwell positions are close to the center as a result of normalizing the distribution at that point. However, when the source is moved toward the distal or proximal ends, the 1.0 cm dose differs on the opposite end. Since the relative dose is small in those areas (on the order of 20%) this effect will not be as significant as the differences close to the balloon surface where the dose is much higher. Closer to the balloon surface, the difference in the doses is more pronounced. This can readily be seen in Fig 10 where the actual dose is larger than the dose determined by the treatment planning system by a factor of 1.5. Since the treatment planning system dose is at times as great as 300% of the prescription dose at the surface, the actual dose can be as much as 500% greater. Furthermore, it appears that the actual distribution is less concentrated than the planning system s distribution. This is a direct result of having a much larger dose at the surface which dissipates over a wider area. Simulations were made for the other Axxent balloon applicators with similar results. However, the 5x7 ellipsoidal applicator displayed the largest discrepancy between actual dose and treatment planning dose distributions. Conclusions Dose distributions computed and experimentally verified in this study are compared with the dose distributions computed by a commercial treatment planning system for the Axxent balloon applicator. Although the two distributions were similar at the 1.0 cm prescription point, they were significantly different close to the surface of the balloon. This was confirmed using a parallel plate extrapolation ionization chamber to accurately measure surface dose. Given this dose differential, the TG-43 anisotropy function F L (r, Ө), and the radial dose function g L (r) that are at present routinely applied cannot accurately account for the variations in applicator size and shape and source dwell 12

13 position. Furthermore, a planning system using the TG-43 formulization without modification will not compute the dose distribution correctly when attenuating material such as a barium impregnated balloon applicator wall, is in the path of the ionizing radiation. 13

14 References [1] D.S. Francescatti, J.W. Rieke, M.J. Rivard, J.P. Williams, S. Axelrod, R.R. Burnside, S.D. Hansen, T.W. Rusch, et al, Concept, Characteristics, and Performance of an Electronic Brachytherapy System for Accelerated Partial Breast Irradiation, Presented at ASBS, (2006) [2] R. Nath, L.L. Anderson, G. Luxton, et al, Dosimetry of interstitial brachytherapy sources: Recommendations of the AAPM Radiation Therapy Committee Task Group 43, Med Phys 22, (1995) [3] M.J. Rivard, B.M. Coursey, L.A. DeWard, et al, Update of AAPM Group No. 43 report: A revised AAPM protocol for brachytherapy dose calculations, Med Phys 31, (2004) [4] M.J. Rivard, S.D. Davis, L.A. DeWerd, et al, Calculated and measured brachytherapy dosimetry parameters for the Xoft Axxent source: An electronic brachytherapy source., Med Phys 2, [5] M.J. Berger, J.H. Hubbell, S.M Seltzer, J. Chang, J.S. Coursey, R.Sukumar, and D.S. Zucker, NIST Standard Reference Database 8 (XGAM), Web Site: [6] M.J. Berger, J.S. Coursey, M.A. Zucker and J. Chang, Stopping-Power and Range Tables for Electrons, Protons, and Helium Ions, Web Site: [7] B. J. Gerbi, F.M. Khan, Measurement of dose in the buildup region using fixedseparation plane-parallel ionization chambers. Med Phys 17, [8] G. Battistoni, S. Muraro, P.R. Sala, F. Cerutti, A. Ferrari, S. Roesler, A. Fasso, J. Randt, FLUKA: a multi-particle transport code Proceedings of the Hadronic Shower Simulation Workshop 2006, Fermilab 6-8 September 2006, M. Albrow, R. Raja eds., AIP Conference Proceedings 896, 31-49, (2007) 14